3.1-1 Configuration and parameters
In our experiment, the technique of hybrid mode-locking is used. We put an EO modulator into the cavity of a passively mode-locked laser and keep the setup all-fiber.
The additive-polarization mode-locking and the EO phase modulation are combined together to achieve the hybrid mode-locking, as shown in Fig 3-1 [19]. In order to get more nonlinearity in the fiber cavity, high intracavity light intensity is needed. As a result, the method of bi-directional pumping is utilized in the experimental setup and about 750mW of 980nm pump is available in the experiment. An EO phase modulator is put in the fiber ring cavity to achieve active mode-locking, and the polarization dependent EO modulator and two polarization controllers provide the mechanism of additive-pulse mode-locking. Because the EO phase modulator in the fiber ring cavity is polarization dependent, it also works as a polarizer. If the EO modulator is replaced with a polarization dependent isolator, the laser becomes a purely passively mode-locked laser.
The isolator in the ring cavity is to ensure the pulses propagate in only one direction. The tunable bandpass filter, whose specifications are shown in Fig 3-2, is used to select the lasing wavelength of the laser. In addition, it can cooperate with the
self-phase modulation（SPM）effect in the cavity to suppress supermodes and to achieve a high supermode suppression ratio（SMSR）. Besides, the 14nm wide bandwidth of the
bandpass filter can support shorter pulses in the cavity so that the generated pulse width also can be shorter.
The output coupler is put behind the Er-fiber to get the greatest output power. The coupling ratio is 30/70 to couple 30% power inside the laser to the laser output. The
chirp of the pulses is compensated with a length of negative group-velocity dispersion
（GVD）fiber.
Our laser can be operated at different states, including the normal active mode-locking, hybrid mode-locking with synchronous and asynchronous modulation.
The devices that have been used in the fiber ring cavity are listed in table 3-1.
1. 980nm pump laser：maximum output power：500mWx1；350mWx1 2. EO phase modulator（from D.C. to 10GHz）
3. Tunable bandpass filter ： 3dB bandwidth Æ 14nm; central wavelengthÆ1540~1560nm
4. WDM coupler
5. Polarization independent isolator 6. Corning SMF-28：about 8m 7. Corning Flexcor fiber：about 5.5m
8. PM panda fiber：located at the EO phase modulator about 4m Table 3-1 Devices in the fiber ring cavity
Fig 3-1 Experimental setup
3.1-2 Results of normal active mode-locking
Our laser is able to work at the state of active mode-locking. The passive mode-locking mechanism is reduced to be very small and the laser now is like a normal active mode-locked laser with little accumulation of the nonlinearity and the pulse width also become larger. The optical spectrum at the normal active mode-locking is shown in Fig 3-2 and the RF spectrum is shown in Fig 3-3. In Fig 3-4 the pulse width from SHG autocorrelation is 4.7ps and the time-bandwidth product is 0.43. In addition,
the supermode suppression ratio（SMSR）is about 50dB.
Fig 3-2 Optical spectrum of normal active mode-locking at 10GHz
repetition rate
0 10G 20G 30G 40G -100
-80 -60 -40 -20
Frequency(Hz)
Fig 3-3 RF spectrum of normal active mode-locking at 10GHz
0 5000 10000 15000 20000 25000
0 2 4 6 8 0 2 4
Delay Time(fs)
10GHz repetition rate
FWHM=4.7ps(Gaussian fitting)
Fig 3-4 The SHG autocorrelation of the pulse at 10GHz under normal
3.1-3 Results of synchronous hybrid mode-locking
If the modulation frequency and the cavity harmonic frequency are the same then the laser is mode-locked by synchronous modulation. The cavity length is about 24m, and the net dispersion of the cavity is about 1.77ps/nm-km. The pulses in the fiber ring cavity are under abnormal dispersion so that the solitons are able to be generated. But in the synchronous condition, the solitons do not occur. One of the reasons may be that the power in the cavity is not enough for the pulses to accumulate large nonlinearity. The other reason may be that the loss for the soliton is larger than that for the Gaussian pulses so that the Gaussian pulse train is produced and the solitons are suppressed.
The optical spectral bandwidth of the output pulses is 1.74nm, shown in Fig 3-5, and the transform-limited pulse width is 1.5ps. This pulse width is still narrower than that produced by the purely active mode-locked lasers. This is because there is still some nonlinearity in the cavity. The output power is 28.6mW and the corresponding peak power is 1.87W. The RF spectrum is shown in Fig 3-6, and the SMSR is about 50dB. Fig 3-7 shows the details of the RF spectrum at 10GHz. The parameters of the mode-locked laser at 10GHz repetition rate are listed in Table 3.1. The autocorrelation of the pulse is shown in Fig 3-8.
Fig 3-5 Optical spectrum at synchronous modulation
9.98G 9.99G 10.00G 10.01G 10.02G -100
-80 -60 -40 -20 0
Frequency(GHz)
50dB
Fig 3-6 RF spectrum at synchronous modulation（center 10GHz, span 50MHz）
9.9979G 9.9980G 9.9981G 9.9982G 9.9983G -100
-80 -60 -40 -20 0
Frequency(GHz)
Fig 3-7 RF spectrum near 10GHz at synchronous modulation
0 5 0 0 0 1 0 0 0 0 1 5 0 0 0 2 0 0 0 0 2 5 0 0 0 3 0 0 0 0
0 2 4 6 8 0
D e la y tim e (fs )
1 0 G re p e titio n ra te F W H M = 1 5 2 7 fs (s e c h ^2 fittin g )
Fig 3-8 The SHG autocorrelation of the pulse at 10GHz under hybrid
mode-locking by synchronous modulation
3.1-4 Results of asynchronous hybrid mode-locking
If the modulation frequency and the cavity harmonic frequency are not the same
（with 20~40kHz deviation）, then the fiber laser is mode-locked by asynchronous
modulation. The method for achieving asynchronous mode-locking is to find the mode frequency precisely first and adjust the frequency of the synthesizer to be 20~40kHz away from the frequency found before. Then we adjust the polarization controllers properly to achieve mode-locking. In this way, whether the modulation frequency is little larger or smaller than the cavity frequency, a stable pulse train with low noise and short pulsewidth can be generated.
Some parameters and results for the laser configuration are presented below. The average output power is 31.4mW and the corresponding peak power is 37W. The optical spectrum is shown in Fig 3-9 with the optical bandwidth is 3.24nm. The autocorrelation of the pulses is shown in Fig 3-10, and the pulse width is 816fs by sech^2 fitting. The autocorrelation is measured by the method of second harmonic generation （SHG）. The
time-bandwidth product is 0.32, which indicates the pulses are nearly transform-limited.
The SHG autocorrelation of the pulses is also very clean with no background.
The RF spectrum of the mode-locked laser is shown from Fig 3-11 to Fig 3-13. Fig 3-11 shows the RF spectrum from 0 to 40GHz, and there are four harmonic frequencies, which indicating 10GHz, 20GHz, 30GHz and 40GHz respectively, shown
in Fig 3-11. The 3rd and 4th harmonic frequencies become smaller due to the response of the amplifier. The first harmonic frequency 10GHz is shown more clearly in Fig 3-12.
The supermode noise is very low and the SMSR is more than 70dB. That is because there are several mechanisms that reduce the supermode noises in the laser cavity. One is the additive-pulse limiting（APL）and the other is the asynchronous mode-locking
（ASM）mechanism. Fig 3-13 shows that the modulation frequency is shifted from the
cavity frequency. The highest peak is where the cavity frequency is located and next to the peak is where the modulation frequency is located. It is obvious that there is deviation between the two frequencies.
Fig 3-9 Optical spectrum at asynchronous modulation
0 5000 10000 15000 20000 25000 30000
Fig 3-10 The SHG autocorrelation of the pulse at 10GHz under
hybrid mode-locking by synchronous modulation
Fig 3-11 RF spectrum from 0Hz to 40GHz at synchronous modulation
Fig 3-12 RF spectrum at asynchronous modulation（center 10GHz, span 50MHz）
9.9978G 9.9979G 9.9980G 9.9981G 9.9982G -100
-80 -60 -40 -20 0
Power( dBm)
Frequency(GHz)
35kHzModulation frequency 1st cavity
harmonic frequency
Fig 3-13 RF spectrum near 10GHz at synchronous modulation
3.1-5 State of bound soliton pulse
We can also observe the state of bound soliton pulses in our laser. This is the phenomenon of pulse splitting with small pulse separation about several picoseconds [20][21].
Fig 3-14 Formation of pulse splitting
If the bound state has the separation of τ0, the field of the bound soliton will
become E(t)=E0(t)+E0(t−τ0)eiθ , where E0(t) and E0(t−τ0) are the two splitted pluses with a phase shiftθ .
We have known the autocorrelation signal can be written as
∫
−= E t E∗ t dt
G1(τ) ( ) ( τ) （3-1）
So the optical spectrum measured by the OSA is
{ }
0 2Therefore there exists sinusoidal modulation on the optical spectrum of the original pulse. The period of the modulation is related to the separation of the bound soliton pulses by equation 3-3. Fig 3-15 shows the measured optical spectrum of the bound
)
0
( t
E
E0(t−τ
0)spectrum. Here the period of modulation is 2.4nm and thus the corresponding separation
τ0 will be 3.38ps. Fig 3-16 shows the autocorrelation of the bound soliton pulses. The apparent three peaks indicate the twin-pulse operation of the laser. The measured separation is 3.68ps and is very close to the estimated value from the period of modulation of the spectrum. To the best of our knowledge, this is the first observation of bound soliton states in hybrid mode-locked fiber lasers.
Fig 3-15 Optical spectrum of bound soliton pulse
Fig 3-15 Optical spectrum of bound soliton pulse
Fig 3-16 Autocorrelation of bound soliton pulses
Fig 3-17 and Fig 3-18 show the RF spectrum of the bound soliton pulses. Because the separation of the splitted pulses is very small（about several picosends）, the output
pulse repetition rate will not increase. Therefore the peak of the mode-locking frequency is not changed and the supermode is also very small. From Fig 3-18 we know the bound state of hybrid mode-locking is under synchronous modulation because there is only one frequency component near the main mode.
9.98G 9.99G 10.00G 10.01G 10.02G -100
-80 -60 -40 -20 0
Frequency(Hz)
Fig 3-17 RF spectrum of bound soliton pulses at 10GHz
（center 10GHz, span 50MHz）
9.9978G 9.9979G 9.9980G 9.9981G 9.9982G
-100 -80 -60 -40 -20 0
Frequency(Hz)
Fig 3-18 RF spectrum of bound soliton pulses near 10GHz（span 500kHz）
3.1-6 Summary
To summarize, the mode-locked fiber laser can work stably by asynchronous modulation and has better performance in terms of shorter pulsewidth and lower supermode noise than synchronous modulation and normally active mode-locking. In asynchronous mode-locked lasers the modulation frequency is adjusted to deviate 20~40kHz from the cavity mode frequency. At this moment, if the modulation frequency is adjusted to approach the cavity mode frequency, the optical spectrum will change. When the modulation is very near to the cavity frequency（deviation is less than 10kHz）, the optical bandwidth will become smaller（about 1.5nm）. When the
modulation frequency is adjusted away the cavity frequency again, the optical spectrum will be restored to the original shape.
Under synchronous mode-locking, the linear pulses will get more gain than solitons. However, the loss of linear pulses increases under asynchronous mode-locking.
As a result, the linear pulses will get less gain than solitons, which makes the laser prefer to work at the soliton state. Another interesting observation is that the achieved pulse width through asynchronous modulation is also shorter than that through synchronous modulation.
3.3 Stabilization of asynchronous hybrid mode-locking
3.2-1 Introduction
Although we have demonstrated a stable pulse train with 10GHz repetition rate and shorter pulsewidth by asynchronous modulation, the fiber laser has the problem of long term stability because of its long cavity length. For the normal harmonic mode-locked lasers, techniques including regenerative mode-locking as well as cavity length dithering can be used to achieve excellent long term stability [22]. Regenerative mode-locking is accomplished by feeding back the self-beat signal and achieved synchronization automatically because the feedback signal reflecting the instantaneous frequency change of the cavity modes. In asynchronous modulation, the regenerative mode-locking method is not applicable because of the desired frequency deviation between the modulation frequency and cavity harmonic frequency. When the frequency deviation oversteps the range of the detuning limit, the mode-locking is destroyed. As time goes by, the cavity frequency will drift due to the effects of temperature changes and the frequency deviation will possibly change too much to hold the mode-locking state. Therefore the method of cavity length dithering is still necessary in the asynchronous modulation in order to achieve long term stabilization. In next subsection we will show the experimental configuration and explain how to achieve the cavity length dithering for asynchronous mode-locked lasers through a new proposed method.
3.2-2 Configuration and parameters
In our experiment shown in Fig 3-19, we demonstrate the cavity length dithering operation of a fiber laser with the cavity length being controlled by a PZT on which part of fiber cavity is wound. The cavity length can be changed by applying a DC voltage to the PZT and thus the drifting of the cavity frequency can be restricted within the limit of the detuning range.
Assuming the cavity length is L , so the corresponding free spectral range（FSR）
of the laser longitudinal mode is
nL
Therefore the amount of the frequency shift is proportional to the variation of cavity length. Particularly if the cavity length increases, the frequency shift will be negative; if the cavity length decreases, the frequency shift will be positive.
Fig 3-20 shows our handmade PZT stretcher whose intrinsic displacement is 17.4±
2μm at 150V DC. Since we have wound 5 circles, the total estimated length stretch is
87 μm. The corresponding frequency shift is
(
th MHz)
kHzBut the actual stretching performance is not as good as the estimated performance because of the real winding strength. The measured linear relation between the input voltage applied on PZT and the obtained frequency shifts is shown in Fig 3-21. The maximum frequency shift is only 26kHz, indicating the maximum length stretch of the PZT stretcher is only 64.5μm.
Fig 3-13 shows that there exist many frequency components in asynchronous modulation with the frequency separation equal to the detuning frequency. The situation near zero frequency is shown in Fig 3-22. This is the RF spectrum from 0Hz to 300kHz and we can also observe many frequency components where the frequency deviation is about 45kHz. Therefore we can utilize these lower frequency components near DC to achieve cavity length dithering without requiring electronic devices at RF frequencies.
To stabilize the asynchronous mode-locked laser we have to prevent the frequency deviation from exceeding the detuning limit by feeding back a signal to control the PZT dithering for producing an intentional frequency shift to compensate the environmental frequency drift. Fig 3-23 shows the configuration of the feedback circuit which comprises a frequency-to-voltage（F/V） converter, proportional and integral feedback
circuits, and a high voltage controller. The detuning frequency is converted into a voltage signal with a F/V converter and then coupled into the voltage comparator. In
this way, an error signal which deviates from a standard voltage is used as an offset signal. When the cavity length is shortened by perturbation under a certain condition, the error signal becomes positive, while it becomes negative when the cavity length is increased. Thus by feeding the error signal of the detuning frequency back to the PZT after it has passed through a proportional and integral control circuit, the frequency deviation of the asynchronous mode-locked laser can be stabilized.
Fig 3-19 The experimental setup of stabilization
Fig 3-20 The picture of handmade PZT stretcher
Fig 3-21 Relation between the input voltage applied on PZT and the obtained
frequency shifts
20 40 60 80 100 120 140 160
5.0k 10.0k 15.0k 20.0k 25.0k 30.0k
frequency(kHz) voltage(V)
30 4.94 60 9.87 90 15.46 120 19.46 150 26.4
Frequency drift =688+140.31905*Voltage+0.19286*Voltage2
Frequency shift(Hz) @10GHz
Input Voltage(V)
Original Value Polynomial Fitting
Fig 3-22 Spectral components of detuning frequency near DC
Fig 3-23 Diagram of the feedback circuit
3.2-3 Results
Before applying the error signal which is fed back to adjust the cavity length, the drifting of the cavity frequency caused by environmental temperature has to be measured. Assuming the temperature expansion coefficient of the single mode fiber is
deg /
10−5 , if the temperature increases 1°C, the fiber length will stretch200µm. With FSR＝10MHz and cavity length＝20m, the cavity frequency may drift by
Hz
Near 10GHz the frequency drift will be kHz MHz
Hz GHz 100
10
100 ×10 = .
This is the possible frequency drift caused by temperature. Fig 3-24 shows the change in the detuning frequency near DC with time. Without stabilization, there was a detuning frequency drift of 17 kHz to 31 kHz over the course of 10 minutes with the temperature at 25℃ and the measured maximum frequency changing rate is 315 Hz/sec. Besides,
the frequency drift is also chaotic and dependent on the temperature very much. Since the possible frequency drift may be up to 100 kHz, the stabilization of the cavity frequency cannot be achieved fully by the stretching of the PZT. So we still need the mechanism of temperature controller. The result of stabilization without temperature controller is shown in Fig 3-25. In the initial 100 seconds the detuning frequency is well-confined within several hundred herz near 27 kHz, but for the long term the detuning frequency will still be out of the control due to the environmental influence.
0 100 200 300 400 500 600
Fig 3-24 Changes in the detuning frequency near DC with time
0 20 40 60 80 100
Fig 3-25 Stabilization of initial 100 seconds
3.3 Discussions
Because of the unstable variation in temperature we have not demonstrated the long term stabilization of the asynchronous mode-locking. But the methods of the cavity length dithering have been reported successfully for normal actively mode-locked laser [23]. The stabilized repetition rate was completely within a few Hz and the stability is better than10−9. Fig 3-26 shows the change in the repetition rate with time. Without stabilization, it changes periodically, which reflects the on/off state of the air conditioner in the room. With stabilization, there is no change in the repetition rate.
Fig 3-26 Changes in the repetition rate of regeneratively mode-locking
Chapter 4：Conclusions and future work
4.1 Summary of achieved results
We have successfully demonstrated a 10GHz femtosecond hybrid mode-locked Er-fiber soliton laser by asynchronous phase modulation. There are two types of possible pulse solutions in the laser ring cavity initially. One is the linear Gaussian pulse state and the other is the nonlinear soliton pulse state. Whether one can obtain the solitons or Gaussian pulses is determined by the modulation frequency (asynchronous or synchronous). On one hand, by detuning the deviation of modulation frequency from the cavity harmonic frequency about 20~40 kHz, the soliton pulse is formed through the asynchronous mode-locking. On the other hand, the Gaussian pulse is formed when the laser is mode-locked with synchronous modulation. According to our experimental results, asynchronous mode-locking shows superior performance than synchronous mode-locking in two aspects. The first one is the higher SMSR and more stable operation. Because the asynchronous modulation and the guiding center soliton effect can reduce the background noises in the cavity, the supermode noise with asynchronous mode-locking is lower than that with synchronous mode-locking. Another aspect is that the pulse-width in the asynchronous mode-locking is much shorter than the one in the synchronous mode-locking. Besides the mechanism of passive mode-locking, ASM is also helpful for obtaining shorter pulses. Since the central wavelength of the pulses will
vary periodically with asynchronous mode-locking, the pulses may experience wider
vary periodically with asynchronous mode-locking, the pulses may experience wider